In this paper, we introduce the notion of crystal bases of KacแMoody superalgebras. We prove the existence of the crystal bases for integrable modules following Kashiwara's grand loop argument and we also prove the tensor product rule for these bases. We simplify his argument without introducing the
A Character Formula for Generalized Kac-Moody Superalgebras
โ Scribed by U. Ray
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 354 KB
- Volume
- 177
- Category
- Article
- ISSN
- 0021-8693
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โฆ Synopsis
In [1], Borcherds defined generalized Kac-Moody (denoted by GKM for short) algebras and gave a character formula for lowest weight modules of these algebras. In this paper we give a character formula for lowest weight modules of GKM superalgebras. For any standard result about contragredient superalgebras that have an immediate generalization to GKM superalgebras see [3] and [4]. All vector spaces are assumed to be over the real field. 1995 Academic Press, Inc
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